Back to EveryPatent.com
United States Patent |
6,199,028
|
Repperger
,   et al.
|
March 6, 2001
|
Detector for human loss of tracking control
Abstract
A device is described which incorporates three components: a tracking error
estimator, a detector, and a red light indicator to alert a pilot to the
potential loss of tracking control. The tracking error estimator uses the
difference between the target and the desired response of the tracking
aircraft to estimate the divergence from a desired tracking path. This
difference is acquired by such systems as, for example, the Global
Positioning System (GPS) and radar. The tracking error and its derivatives
are then converted into three different metrics. The metrics represent
percentage points when the tracking error and its derivatives are in an
unstable or stable portion of its phase plane. Depending upon whether
these metrics and/or their combinations are above a particular threshold,
the detector and indicator will alert the pilot or operator whether or not
corrective action needs to be taken. The threshold is determined by a
predetermined logic tree. This system has applicability in a variety of
tracking scenarios involving pilots or simulator system operators. Pilots,
when they fly tactical aircraft, are preoccupied in a number of different
tracking tasks which can be assisted by the invention described herein.
Inventors:
|
Repperger; Daniel W. (Dayton, OH);
Haas; Michael W. (Beaver Creek, OH)
|
Assignee:
|
The United States of America as represented by the Secretary of the Air (Washington, DC)
|
Appl. No.:
|
244828 |
Filed:
|
February 4, 1999 |
Current U.S. Class: |
702/189; 244/3.1; 244/221; 701/3; 701/122; 702/94 |
Intern'l Class: |
G06F 017/00; F41G 007/00 |
Field of Search: |
702/94,95,150,189
701/3,116,120,122,213-214
244/3.1,3.11,195,220,221
700/28,43,45,80
|
References Cited
U.S. Patent Documents
3832065 | Aug., 1974 | Sullivan et al. | 356/210.
|
4092716 | May., 1978 | Berg et al. | 701/3.
|
4269512 | May., 1981 | Nosler | 356/375.
|
4477043 | Oct., 1984 | Repperger | 244/223.
|
4536866 | Aug., 1985 | Jerome et al. | 369/112.
|
4773055 | Sep., 1988 | Gijzen et al. | 369/45.
|
5016177 | May., 1991 | Lambregts | 244/181.
|
5062594 | Nov., 1991 | Repperger | 701/3.
|
5101472 | Mar., 1992 | Repperger | 700/261.
|
5353226 | Oct., 1994 | Repperger et al. | 364/433.
|
5629848 | May., 1997 | Repperger et al. | 364/424.
|
5651512 | Jul., 1997 | Sand et al. | 244/3.
|
Primary Examiner: Hoff; Marc S.
Assistant Examiner: Bui; Bryan
Attorney, Agent or Firm: Tollefson; Gina S., Hollins; Gerald B., Kundert; Thomas L.
Goverment Interests
RIGHTS OF THE GOVERNMENT
The invention described herein may be manufactured, used, sold, imported,
and/or licensed by or for the Government of the United States of America
without the payment of any royalties thereon.
Claims
What is claimed is:
1. A method for detecting potential loss of tracking control between a
tracker unit and a target trajectory comprising the steps of:
calculating a tracking error from a position indicator means, the tracking
error being the difference between the target trajectory and a desired
response of the tracker unit;
estimating the tracking error and derivatives of the tracking error in a
phase plane; and
detecting whether the tracking error is divergent.
2. The method of claim 1 wherein the difference between the target
trajectory and the desired response of the tracker unit is calculated from
information provided by a system selected from the group consisting of
Global Positioning System (GPS), radar, Airborne Warning and Control
System (AWACS), data link, video source, landing approach aid, specified
flight path trajectory, or a satellite.
3. The method of claim 1 further comprising the step of alerting an
operator of the tracker unit when the tracking error is divergent.
4. The method of claim 3 further comprising the steps of:
calculating percentage points when the tracking error and its derivatives
are in selected portions of the phase plane;
calculating whether the percentage points in selected portions of the phase
plane exceed a predetermined threshold indicating loss of tracking
control; and
detecting when the predetermined threshold is exceeded.
5. The method of claim 4 wherein a logic tree is used to detect when the
predetermined threshold is exceeded.
6. The method of claim 1 wherein calculating whether the tracking error is
divergent is determined when a trajectory of the tracking error is in
either of two quadrants of a four-quadrant phase plane.
7. The method of claim 6 wherein the trajectory is calculated to be
divergent if one of the following conditions are met: the trajectory is in
a wholly positive quadrant of the phase plane, independent and dependent
variables are in both positive or negative quadrants of the phase plane,
and independent and dependent variables are both negative.
8. The method of claim 1 wherein the estimation of the tracking error and
its derivatives of said estimating step is done by calculating state
variables for the tracking error and its derivatives by filtering the
tracking error and its derivatives through a low-pass filter.
9. An apparatus for detecting potential loss of tracking control between a
tracker unit and a target comprising:
means for calculating a tracking error from a position indicator means, the
tracking error being the difference between the target and a desired
response of the tracker unit;
means for estimating the tracking error and derivatives of the tracking
error in a phase plane; and
means for detecting whether the tracking error is divergent.
10. The apparatus of claim 9 wherein the means for calculating the
difference between the target and the desired response of the tracker unit
receives input data from a system selected from the group consisting of
Global Positioning System (GPS), radar, Airborne Warning and Control
System (AWACS), data link, video source, landing approach aid, specified
flight path trajectory, or a satellite.
11. The apparatus of claim 9 further comprising means for alerting an
operator of the tracker unit when the tracking error is divergent.
12. The apparatus of claim 11 further comprising:
means for calculating percentage points when the tracking error and its
derivatives are in selected portions of the phase plane;
means for calculating whether the percentage points in selected portions of
the phase plane exceed a predetermined threshold indicating loss of
tracking control; and
means for detecting when the predetermined threshold is exceeded.
13. The apparatus of claim 12 wherein the means for detecting when the
predetermined threshold is exceeded is a processor programmed with a logic
tree.
14. The apparatus of claim 9 wherein the means for calculating whether the
tracking error is divergent includes means for determining when a
trajectory of the tracking error is in either of two quadrants of a
four-quadrant phase plane.
15. The apparatus of claim 14 wherein the means for determining when the
trajectory of the tracking error is in either of two quadrants of a
four-quadrant phase plane includes means for determining if one of the
following conditions are met: the trajectory is in a wholly positive
quadrant of the phase plane, independent and dependent variables are in
both positive or negative quadrants of the phase plane, and independent
and dependent variables are both negative.
16. The apparatus of claim 9 wherein the means for estimating the tracking
error and its derivatives includes means for calculating state variables
for the tracking error and its derivatives by low pass filtering means.
17. The apparatus of claim 9 wherein the means for estimating the tracking
error and its derivatives includes a summer and at least one integrator
connected in series through a feedback circuit.
18. The apparatus of claim 17 wherein the summer is an inverting, adder
operational amplifier circuit and said integrator is an inverting
integrator operational amplifier circuit.
19. The apparatus of claim 18 further comprising an alarm means which is
activated when the means for detecting whether the tracking error is
divergent detects that the tracking error is divergent.
Description
FIELD OF THE INVENTION
This invention relates to the field of aircraft pilot assistance systems
and more particularly to systems that detect tracking errors.
BACKGROUND OF THE INVENTION
Devices that help pilots fly aircraft in unusual environments and
circumstances are necessary as the performance characteristics of aircraft
steadily increase. An example of one such device is described in U.S. Pat.
No. 5,353,226, issued to D. W. Repperger on May 7, 1996 and entitled,
"Coriolis Indicator For Situational Awareness." The device described in
this U.S. Patent uses measurements of angular rates (aircraft body axis
rates) and an indicator to detect the existence of Coriolis accelerations
which may not be immediately obvious to a pilot. The presence of Coriolis
accelerations affects a pilot's perception of aircraft attitude and
spatial orientation, thus potentially affecting the safety of the pilot.
Another example of a pilot assistance device is described in U.S. Pat. No.
5,629,848, issued to Repperger et al on May 13, 1997 and entitled,
"Spatial Disorientation Detector." This detector senses important
acceleration fields that are known to produce spatial disorientation to a
pilot. This detector utilizes implicit models of the human vestibular
system and a Kalman filter estimator to examine when adverse environmental
influences may exist, even though these influences may not be readily
detected by the pilot.
Examples of other pilot assistance devices and/or methods are found in the
following articles: R. F. Stengel, "Toward Intelligent Flight Control,"
IEEE Transactions on Systems, Man, and Cybernetics, vol. 23, No. 6,
November/December 1993, pp. 1699-1717; T. B. Sheridan and W. R. Ferrell,
"Man-Machine Systems: Information, Control, and Decision Models of Human
Performance," The MIT Press, Cambridge, Mass., 1974; R. A. Hess, "Effects
of Time Delays on Systems Subject To Manual Control," J. Guidance,
July-August, 1984, pp. 416-421; and R. A. Hess, "Technique For Predicting
Longitudinal Pilot-Induced Oscillations," J. Guidance, vol. 14, no. 1,
1990, pp. 198-204.
There still exists a need in these arts to not only notify the pilot of
adverse conditions, but also to assist the pilot in tracking tasks. These
tasks include pursuit or chase of another aircraft wherein the
minimization of the error between position and orientation of the two
aircraft is critical, following a specified flight trajectory or flight
path, or following a specified terrain or runway. The present invention
addresses this need.
SUMMARY OF THE INVENTION
Accordingly, one general object of the present invention is to provide a
method and device that will assist a pilot in tracking various objects,
and/or flight path, and/or terrain when flying. Another object of the
present invention is to aid pilot training when over-control, and
associated pilot-induced oscillation in pitch and/or roll is present. A
third object of this invention is to aid operators of uninhabited vehicles
when flying a specified flight path using a video feed from the vehicle to
the ground-based control station.
Generally, the present invention is a device and method which includes a
tracking error estimator, a detector and an indicator to alert the pilot
to the potential loss of tracking control. The tracking error estimator
uses the difference between the target and the desired response of the
tracking aircraft to estimate the divergence from a desired tracking path.
This difference is acquired by such systems as the Global Positioning
System (GPS), radar, data link, video source, etc. The tracking error and
its derivatives are then converted into 3 different metrics. The metrics
represent percentage points when the tracking error and its derivatives
are in an unstable or stable portion of its phase plane. Depending on
whether these metrics and/or their combinations are above a particular
threshold, the detector and indicator will alert the pilot or operator
whether or not corrective action needs to be taken. The threshold is
determined by a predetermined logic tree.
The present invention anticipates a different type of detection system than
those previously disclosed. The present invention monitors and identifies
instabilities that may occur in the tracking of either moving or
stationary targets. The purpose of the present invention is to provide a
pilot in an aircraft, or an operator of a remote aircraft simulation
system, an improved awareness of the possibility that the tracking error
is about to diverge. In one embodiment of the invention, a red light
indicator will illuminate, indicating that sudden changes have to be made
because the tracking error will suddenly get larger and that loss of
control is possible. Such a device provides an alerting mechanism to the
pilot or operator of a ground-based tracking system of the imminent loss
of control of the tracking task. The pilot or person involved in the
tracking task may wish to modify the aircraft's characteristics or make
other adaptive changes in order to improve the performance of the mission
at hand. The apparatus described herein will also be helpful in predicting
the incidence of a pilot-induced oscillation (PIO). PIO commonly occurs
when pilots test new aircraft, and represents one of the first indications
of loss of control of the aircraft. Finally, another possible application
of the present invention may be to help establish a decision rule for an
automated system to take over control of an aircraft when some undesirable
event is about to produce a large tracking error. This device can also be
used to predict a sudden change in error when landing an aircraft or when
tasked with the mission of following terrain or other targets fixed in
space.
BRIEF DESCRIPTION OF THE DRAWINGS
These and other features of the invention will be understood in light of
the ensuing detailed description of the invention and the attached
figures, wherein:
FIG. 1 is a generic diagram of the method according to the present
invention;
FIG. 2 is a diagram of a phase plane showing four examples of various
trajectories within the phase plane;
FIG. 3 illustrates an alternative phase plane plot of (d.sup.2
e)/(dt.sup.2) versus (de)/(dt);
FIG. 4 depicts a plot of (d.sup.3 e)/(dt.sup.3) versus (d.sup.2
e)/(dt.sup.2);
FIG. 5 illustrates one embodiment of an estimator according to the present
invention;
FIGS. 6a and 6b are diagrams showing operational amplifier circuitry of two
elements of the estimator according to the present invention;
FIG. 7 illustrates data from a pitch axis indicating pilot induced
oscillation (PIO) in experimental aircraft;
FIGS. 8a, 8b, and 8c illustrate a synthesized phase plane plot describing a
sinusoidal e(t) signal (during a PIO) within the context of FIG. 1;
FIG. 9 illustrates the detector according to the present invention;
FIG. 10 illustrates the closed-loop tracking error of an operator in a
controllable situation (very low time delay);
FIG. 11 illustrates the closed-loop tracking error of an operator during
uncontrollable oscillations or divergent behavior (precipitated by a 600
millisecond time delay and with turbulence noise added to the closed-loop
simulation);
FIGS. 12a, 12b, and 12c are the three phase planes of interest for a stable
tracking situation; and
FIGS. 13a, 13b, and 13c are the same phase plane plots as in FIGS. 12a-12c
for an unstable tracking situation.
DETAILED DESCRIPTION OF THE INVENTION
FIG. 1 illustrates a generic device and method according to the present
invention which is useful in detecting tracking error instability. The
variable f.sub.t shown in FIG. 1 represents the target trajectory of the
tracked object which could be another aircraft (moving target), or a
stationary target such as a landing path, a terrain following scenario, or
any other non-moving target. The output of the human-machine system is
f.sub.p which represents the tracking aircraft's output, i.e., its
position and orientation, in response to f.sub.t. The term human-machine
system, as used throughout the remainder of this description, means the
interactive system of a human being flying or operating an aircraft. A
transfer function H(s) is used in FIG. 1 to characterize the combination
of pilot-aircraft dynamics. The tracking error e(t) represents the
difference between the target and the desired response of the tracking
aircraft, which is ideally f.sub.p =f.sub.t, but the more practical case
is (f.sub.p.noteq.f.sub.t). A nonzero error, such as (e(t)=f.sub.t
-f.sub.p), is more likely to result.
It is common knowledge that in modem aircraft systems both the measurements
of f.sub.p and f.sub.t are available. They can be calculated from systems
such as Global Positioning System (GPS), radar, the Airborne Warning and
Control System (AWACS) (another aircraft to pinpoint objects in the combat
arena), or from various sensor-laden satellites. In addition, f.sub.t can
be a specified flight trajectory, such as a navigation route or a landing
approach. Thus, knowledge of f.sub.p, f.sub.t, and e(t) are available,
on-line, in real time.
In accordance with the present invention, a tracking error estimator
provides a high degree of accuracy in estimating the tracking error. With
this tracking error estimator, a detector and indicator are fashioned to
alert a pilot (or tracker in a ground based system) to potential problems.
For example, if it is determined that a divergence of the tracking error
is about to occur, an automated system could take control of the aircraft
from the pilot and fly safely when the pilot may not be capable.
To specifically understand how error divergence can be predicted, two
methods of analyzing this process will now be described. The first method
deals with "phase plane" plots of the closed-loop error signal e(t). Three
different types of phase plane plots are utilized and the instability
information can be culled from these plots using a relationship derived
from a Euler's approximation of the closed-loop pilot-aircraft dynamics.
Euler's method is borrowed from studies involving numerical approximation
theory. The second method studies the magnitude and phase characteristics
of the closed-loop tracking error at the brink of instability (termed a
"pilot-induced oscillation" or PIO). The second technique will be
described to develop concurrence with the first method (phase plane
approach) and is useful in explaining how to detect a pilot-induced
oscillation. Both of these methods are then used in accordance with the
present invention.
Method 1--Phase Plane Analysis Techniques
In FIG. 2, a diagram of a "Phase Plane" is plotted and FIG. 8 illustrates a
synthesized phase plane plot. The independent variable (horizontal axis)
is the variable e(t) or tracking error. The dependent variable (vertical
axis) is the time derivative or (d/dt)e(t) quantity. The term "phase
plane" arose from early studies in electrical engineering when a plot of a
sine wave versus a cosine wave would yield a circle or the elliptical
diagrams shown in FIG. 8a. The phase angle between these two signals could
be directly read off the figure as plotted and, hence, it provided a
framework to obtain a phase angle between two different time signals.
Thus, the term "phase plane" was developed. To extrapolate this concept
further, FIG. 8b illustrates an alternative phase plane plot of (d.sup.2
e)/(dt.sup.2) versus (de)/(dt). Generalizing this concept even further,
FIG. 8c depicts a plot of (d.sup.3 e)/(dt.sup.3) versus (d.sup.2
e)/(dt.sup.2). It is necessary to utilize all of the FIGS. 8a-8c to
explain the concept of instability because they incorporate both the
magnitude and sign of the error signal (involving its respective
derivatives). To better understand the types of trajectories that appear
in FIGS. 2, 3 and 4, the relationship between the commonly used Euler's
law in numerical integration and the classification of the types of
trajectories that can occur in FIGS. 2, 3 and 4 must be explained.
Euler's Law and its Relationship to FIGS. 2, 3 and 4
In studies on numerical integration, e.sub.t+.DELTA.t represents a data
sample of the closed-loop error signal at the time sample t+.DELTA.t and
e.sub.t represents this quantity at time t. Euler's law taken to a first
order approximation yields:
e.sub.t+.DELTA.t =e.sub.t +(de.sub.t /dt)(.DELTA.t) (1)
which can be considered as a first order Taylor's series expansion of the
error signal about a nominal trajectory.
Equation (1) used in conjunction with the response trajectories of the
different quadrants of the phase plane diagrams in FIGS. 2, 3 and 4 can
classify unstable and stable types of tracking behavior in a very simple
manner. These response trajectories can be broken into two major
divisions: (1) stable responses, which occur in Quadrants II and IV and
(2) unstable responses, which occur in Quadrants I and III.
In FIGS. 2, 3, 4, each of the phase planes is divided into four quadrants
as indicated. It will be shown that trajectories moving into Quadrants II
and IV of FIGS. 2, 3, and 4 always lead to stable responses and
trajectories moving into Quadrants I and III always lead to unstable
responses.
Stable Responses (Trajectories That Move Into Quadrants II and IV):
Using FIG. 2 and equation (1), consider first a trajectory that enters
Quadrant II.
Quadrant II:
In Quadrant II, e.sub.t <0, and (d/dt) e.sub.t >0. However, it is known
from Euler's law that: e.sub.t+.DELTA.t =e.sub.t +(de.sub.t /dt).DELTA.t,
and since .DELTA.t>0, it follows that
.multidot.e.sub.t+.DELTA.t.multidot.<.multidot.e.sub.t.multidot. where,
.multidot.. .multidot. indicates the length or distance measure of a
vector (the square root of the sum of the squares of its components).
Thus, the magnitude of the error at time step t+.DELTA.t is less than the
magnitude of the error at time step t. Hence, the magnitude of the error
signal is decreasing in time and the tracking error is under control or
converging. This same reasoning applies if the trajectory enters Quadrant
IV of FIG. 2.
Quadrant IV
In Quadrant IV, e.sub.t >0 and (d/dt) e.sub.t <0. Again, using the Euler's
relationship e.sub.t+.DELTA.t =e.sub.t +(de.sub.t /dt).DELTA.t, and of
course, since .DELTA.t>0, then, again
.multidot.e.sub.t+.DELTA.t.multidot.<.multidot.e.sub.t.multidot. and the
magnitude of the error signal is decreasing. This is a manifestation of
stable tracking behavior. The alternative to this type of interaction
occurs for trajectories entering Quadrants I and III.
Unstable Responses (Trajectories That Move Into Quadrants I and III)
The same reasoning is repeated for trajectories that enter Quadrant I in
FIG. 2.
Quadrant I
Here, e.sub.t >0 and (d/dt) e.sub.t >0. Again, invoking the Euler's
relationship e.sub.t+.DELTA.t =e.sub.t +(de.sub.t /dt).DELTA.t with
.DELTA.t>0, it follows that in this case,
.multidot.e.sub.t+.DELTA.t.multidot.>.multidot.e.sub.t.multidot., and
error trajectory is diverging and can only get worse. This same effect is
noticed for trajectories that enter Quadrant III of FIG. 2.
Quadrant III
In this quadrant, e<0 and (d/dt) e<0. Again, using e.sub.t+.DELTA.t
=e.sub.t +(de.sub.t /dt).DELTA.t with .DELTA.t>0, it follows that in this
case that
.multidot.e.sub.t+.DELTA.t.multidot.>.multidot.e.sub.t.multidot., and the
error trajectory is diverging in a negative sense. These results also
apply to the higher order derivative phase planes in FIGS. 3 and 4 and the
same reasoning is used to extrapolate this concept to the next two
figures.
Extrapolation of These Results To FIG. 3
To apply this concept to a higher order phase plane, equation (1) can be
rewritten in the form of higher derivative quantities as follows:
(d/dt)e.sub.t+.DELTA.t =(d/dt)e.sub.t +(d.sup.2 e.sub.t /dt.sup.2).DELTA.t
(2)
Equation (2) is now used in lieu of equation (1) and the trajectories that
enter Quadrants I and III in FIG. (3) lead to divergence behavior and
trajectories that enter Quadrants II and IV in FIG. 3 lead to stable
behavior. These results also extend to FIG. 4.
Extrapolation of Results To FIG. 4
To apply this concept to a further, higher-order phase plane, equation (2)
can be rewritten in the form of higher derivative quantities as follows:
(d.sup.2 /dt.sup.2)e.sub.t+.DELTA.t =(d.sup.2 /dt.sup.2)e.sub.t +(d.sup.3
e.sub.t /dt.sup.3).DELTA.t (3)
Equation (3) is now used in lieu of equation (2) and similarly, the
trajectories that enter Quadrants I and III in FIG. 4 lead to divergent
behavior and the trajectories that enter Quadrants II and IV lead to
stable behavior. This detection method according to the present invention
has been validated experimentally with data from a tracking experiment, as
will be explained in more detail further in this detailed description.
Estimator Element as a Method
According to the present invention, the estimator element can be fashioned
as a method embodied in software or hardware. The measurement of the
signal e(t) is used as stated above and its three derivatives are
estimated using a processor through numerical filtering techniques,
described below.
First, let a variable e be defined which will be a low pass filtered
estimate of e based on available data. This yields a transfer function:
e/e=(1)/(1+s/.alpha.).sup.3 (4)
where e is an estimate of e(t), and e(t) is the measured time series (error
signal), s is the Laplace transform variable, and a is the low pass filter
breakpoint. Equation (4) can be rewritten as:
e/e=(.alpha..sup.3)/(s.sup.3 +3.alpha.s.sup.2 +3.alpha..sup.2
s+.alpha..sup.3) (5)
Under steady state conditions in the time domain, equation (5) can be
further expressed as:
(d.sup.3 e/dt.sup.3)+3.alpha.(d.sup.2 e/dt.sup.2)+3.alpha..sup.2
(de/dt)+.alpha..sup.3 e=.alpha..sup.3 e (6)
To assist in the estimation of e and its higher derivatives, state
variables (x.sub.1, x.sub.2, and x.sub.3) are mathematically defined as:
x.sub.1 :=e (7)
x.sub.2 :=(d/dt)e (8)
x.sub.3 :=(d.sup.2 /dt.sup.2)e (9)
with resulting state equations:
(d/dt)x.sub.1 =x.sub.2 =(d/dt)e (10)
(d/dt)x.sub.2 =x.sub.3 =(d.sup.2 /dt.sup.2)e (11)
(d/dt)x.sub.3 =-3.alpha.x.sub.3 -3.alpha..sup.2 x.sub.2 -.alpha..sup.3
x.sub.1 +.alpha..sup.3 e (12)
or
(d/dt)x.sub.3 =-3.alpha.(d.sup.2 e/dt.sup.2)-3.alpha..sup.2
(de/dt)-.alpha..sup.3 (e)+.alpha..sup.3 e (13)
To integrate equations (10), (11), and (12), a first order Euler
approximation is used on these state variables as follows:
x.sub.it+.DELTA.t.apprxeq.x.sub.it +(d/dt)x.sub.it.DELTA.t (14)
where x.sub.it represents the state component xi at time sample t
(i=1,2,3). The initial conditions on the state variables of this filter
are given by:
x.sub.1 (t.sub.0)=e(t.sub.0)=e(t.sub.0) (15)
x.sub.2 (t.sub.0)=(d/dt)e(t.sub.0).apprxeq.(e(t.sub.1)-e(t.sub.0))/.DELTA.t
(16)
x.sub.3 (t.sub.0)=(d.sup.2
/dt.sup.2)e(t.sub.0).apprxeq.[(de(t.sub.1)/dt)-(de(t.sub.0)/dt)]/
.DELTA.t.apprxeq.[e(t.sub.2)-2e(t.sub.1)+e(t.sub.0)]/(.DELTA.t).sup.2
(17)
Thus, the state variables x.sub.1, x.sub.2, and x.sub.3 represent low pass
filtered estimates of e(t), (d/dt)e(t), and (d.sup.2 /dt.sup.2)e(t),
respectively. They are available on-line in real time once e(t) is
calculated using the data available from system such as GPS. These state
variables can then be used to detect whether the tracking error is
diverging or not. Given the above disclosure, one skilled in the art could
derive any number of means of implementing such an method of estimating
the tracking error.
Estimator Element as an Apparatus
The above-described method can also be implemented as an apparatus, i.e.,
hardwired into circuitry. FIG. 5 illustrates the present invention using
the low pass filtering algorithm described in the previous section. As
shown in FIG. 5, the state variables are outputs 530, 545, and 560 of the
integrators 520, 535, and 550.
In operation, the time series (measured) e(t) enters as an input 500 at the
left side of the diagram (the box enclosed inside the dotted lines in this
figure). The estimated variables e(t) 560, (d/dt)e(t) 545, (d.sup.2
/dt.sup.2)e(t) 530 and (d.sup.3 /dt.sup.3)e(t) 515 leave the dotted line
box on the right side of this diagram which drives the next stage of this
system, the detector. The circuitry within the dotted line box acts as a
low pass filter and an estimator. This circuitry is comprised of a summer
510 and integrators 520, 535, 550 which are fed back to the summer 510.
The value of the signal fed back to the summer is 525 (3.alpha.) from
integrator 520, 540 (3.alpha..sup.2) from integrator 535, and 555
(.alpha..sup.3) from integrator 550. The value of a is the bandwidth of
the low pass filter (the combination of the integrators) which can be
adjusted depending on the characteristics of the incoming signal 500,
e(t). Typically in laboratory applications, .alpha.=5 radians/second or
lower is quite appropriate for human tracking signals. Using the apparatus
shown in FIG. 5 necessarily creates a causality between what is measured
and what is estimated. As those skilled in the art will appreciate,
equations (10) and (11) can be verified using this hardware
implementation. Further, equations (12)-(13) are satisfied, at the summer
510 in FIG. 5, by:
(d/dt)x.sub.3 =-3.alpha.(d.sup.2 e/dt.sup.2)-3.alpha..sup.2
(de/dt)-.alpha..sup.3 e+.alpha..sup.3 e (18)
FIGS. 6a and 6b show the summer and integrator elements of the invention as
shown in FIG. 5, respectively, using operational amplifier (OP AMP)
circuits that are commercially available. FIG. 6a is an inverting adder
operational amplifier. Any number of input signals 600 and 605 can be
summed using this configuration and the ratio in which they are added is
selected by the choice of the input resistors 615 and 620, nominally 10 k.
The two input resistors 615 and 620 are shown in parallel being input
through a single input into OP AMP 635. The resistors are all connected to
the common or summing point of the circuit. The input resistors can have
any values depending on the application of the present invention. FIG. 6b
shows a inverting integrator operational amplifier circuit 725 which can
be used for the integrators shown in FIG. 5. The OP AMPS 725 are employed
as high gain isolation devices using the resistor 710 in series with the
capacitor 720. Both of these circuits are well known in the art.
Detector Element
Before the detector element of the present invention is described, it is
important to describe what happens to the human-machine system at the
brink of instability in order for one skilled in the art to understand how
to build the detector element. The key point is to discern between
tracking behavior which is under control and tracking behavior which is
either oscillatory or on the verge of divergence. This done primarily
through the second method of analysis.
Analysis of a PIO and the Detection Algorithm
When a human-machine system is at the brink of instability, a pilot-induced
oscillation (PIO) may occur. This problem was first noted by the Wright
Brothers as it occurred in the pitch axis on the first aircraft. Since
this time, on every new experimental aircraft under testing, some
incidence of this behavior has been recorded. This event occurs primarily
because test pilots, by the very nature of their mission, push new
aircraft to their performance limits, thus precipitating this type of
problem. In recent times, PIOs are known to occur without a pilot's
recognition of the problem, resulting in crashes which could have been
averted if a detector, as described in this application, could have
alerted the pilot to this situation.
For example, FIG. 7 illustrates data from a pitch axis PIO in the
experimental aircraft (YF-22) which crashed one of the two prototypes
built costing the U.S. Air Force over one billion dollars. From this data,
the closed-loop tracking error exhibits sinusoidal type behavior during a
PIO with frequency of oscillation less than 1 Hz.
FIGS. 8a-8c illustrate a synthesized phase plane plot describing a
sinusoidal e(t) signal (during a PIO) within the context of FIG. 1. To
examine this problem in further detail, the assumption is made that the
major component of the e(t) signal can be represented by the time
function:
e(t)=A sin .omega.t (19)
The derivatives of e(t) are then specified as follows:
(de/dt)=A.omega. cos .omega.t (20)
(d.sup.2 e/dt.sup.2)=-A.omega..sup.2 sin .omega.t (21)
(d.sup.3 e/dt.sup.3)=-A.omega..sup.3 cos .omega.t (22)
In FIGS. 8a-8c, the elliptical diagrams are illustrated which apply to
equations (19)-(22). They are all similar in shape with an eccentricity
(ratio of the minor to major axes) of (1/.omega.) and A being a constant.
Time is parametric on the plots and with some effort, one can see that on
a percentage basis, the number of data points that fall in quadrants I and
III during a complete cycle will satisfy the rule (for all the FIGS.
8a-8c) that a percentage of points in Quadrants I and III at the incidence
of a PIO is equal to 50%.
Thus according to the present invention, a decision rule or logic tree to
detect whether or not tracking error instability is about to occur is
based on the measurement of the following three metrics (r.sub.1, r.sub.2,
and r.sub.3), which are derived from the percentage points in any one
quadrant:
To derive these metrics, let r.sub.1 be defined as the percentage of points
in Quadrants I and III in FIG. 8a (the (de/dt) versus e phase plane; let
r.sub.2 be defined as the percentage of points in Quadrants I and III in
FIG. 8b (the (d.sup.2 e/dt.sup.2) versus (de/dt) phase; and let r.sub.3 be
defined as the percentage of points in Quadrants I and III in FIG. 8c (the
(d.sup.3 e/dt.sup.3) versus (d.sup.2 e/dt.sup.2) phase plane).
Clearly at a PIO condition (and for a perfect error sine wave), r.sub.1
=0.5, r.sub.2 =0.5, and r.sub.3 =0.5. At an instability, it is easy to
show that r.sub.1 >0.5, r.sub.2 >0.5, and r.sub.3 >0.5. As an example of a
detection scheme, the present invention anticipates the following
methodology:
(M-1)(1) Check if either r.sub.1 >0.5, or r.sub.2 >0.5, or r.sub.3 >0.5.
(23)
(M-2)(2) If (M-1) is true, then check if r.sub.1 r.sub.2 >0.25, r.sub.1
r.sub.3 >0.25, or r.sub.2 r.sub.3 >0.25. (24)
(M-3)(3) If (M-2) is true then check if r.sub.1 r.sub.2 r.sub.3 >0.125.
(25)
For a conservative detector, the rule could be that if (M-3) is satisfied,
a red light indicator would go on to warn the pilot of a potential
instability. If the data were more noisy and a less conservative scheme
was desired, the detection rule could be to turn on the red light if (M-2)
or (M-3) were true. For a more liberal design, the detector would turn on
the red light if either (M-1), or (M-2) or (M-3) were to be satisfied.
FIG. 9 illustrates the present invention including the generic detector
system as described above. Those skilled in the art will readily
appreciate that this detector system can be made in any number of ways
using existing commercial devices and/or software. As shown, the four
outputs of the estimator shown in FIG. 5 are input into a computer or
processor 900 in order to compute the values of r.sub.1, r.sub.2, and
r.sub.3. These values are then input into another computer or processor
905 or referred through the computer or processor 900 to analyze the
conditions as set forth above. Depending on whether there is an error in
tracking and depending on the logic tree selected, an indicator, such as
light, alarm, or similar means, would activate or not.
Experimental Data
To provide those skilled in the art with a validation of the present
invention, data from an experiment will be described. Data was collected
to validate the present invention. Using the system described in FIG. 1, a
time delay was added to the stick output of the operator. This delay
affected the response time between a command on the joystick and its
effect in the change of the response of the tracking aircraft (f.sub.p in
FIG. 1). The experimental paradigm, involving human tracking, consisted of
increasing the time delay until the overall human-machine system went into
oscillation. It is noted that roll and pitch noise were also added to the
simulation to help trigger a PIO. Studies in human-machine systems have
demonstrated that for a sufficiently long time delay, human tracking
behavior changes from a continuous form of movement to discrete (wait and
see) movements. When the time delay gets sufficiently large (with
turbulence noise added in both the pitch and roll axis), the overall
system goes into oscillations, or there is a complete loss of tracking
control. This is a well-known effect documented in the aeronautical
literature of the occurrence of phenomena of this type.
FIG. 10 illustrates the closed-loop tracking error of an operator in a
controllable situation (very low time delay) and FIG. 11 illustrates this
same subject during uncontrollable oscillations or divergent behavior
(precipitated by a 600 millisecond time delay and with turbulence noise
added to the closed-loop simulation). FIGS. 12a-12c are the three phase
planes of interest for the stable tracking situation and FIGS. 13a-13c are
these same phase plane plots for the unstable tracking situation. It is
useful to compare the scales of the respective axes, as well as the
trajectory shapes, when discerning differences between FIGS. 12a-12c and
13a-13c. Table I compares the r.sub.1, r.sub.2, and r.sub.3 values with
their respective product terms for controllable tracking versus
uncontrollable tracking. As those skilled in the art will appreciate,
comparisons between these values in Table I to the phase plane plots of
FIGS. 12a-12c and 13a-13c are revealing.
TABLE I
r.sub.1, r.sub.2, and r.sub.3 Values for Stable and Unstable Tracking
Behavior
Tracking
Mode r.sub.1 r.sub.2 r.sub.3 r.sub.1 r.sub.2 r.sub.2 r.sub.3
r.sub.1 r.sub.3 r.sub.1 r.sub.2 r.sub.3
Stable 0.429 0.117 0.145 0.050 0.017 0.062 0.007
Tracking
Unstable 0.754 0.226 0.251 0.170 0.056 0.189 0.043
Tracking
Comparison of the respective quantities (r.sub.1, r.sub.2, and r.sub.3) as
described in equations (24)-(26) indicate a relative concurrence between
the decision rules as explained in (27)-(29) with the data portrayed in
Table I with values about one-half those theoretically predicted for a
PIO. Comparing between rows 1 and 2 of Table I, however, makes it possible
to distinguish between the two types of tracking behavior. The term
r.sub.1 r.sub.2 r.sub.3 shows the greatest relative method of
distinguishing between these two modes of tracking behavior as manifested
by these metrics.
Finally, as a caveat to this approach, it is noted than any decision
mechanism is prone to false positives and missed negatives (type I and II
error). The level of conservativeness of the detector can be varied (via
the choice of rules in equations (27)-(29)) such that an adjustment can be
made by the operator on his need to be alerted to the possible loss of
tracking control. Obviously, increasing the sensitivity to potential
instability would lead to more incidents of false positives and vice
versa.
Also the presumption that Euler's method could be used to characterize the
closed-loop error of the human-machine system as a first order system may
be questioned. This assumption is equivalent to the transfer function in
FIG. 1 to be approximated by:
H(s)=f.sub.p /e.apprxeq..omega..sub.c /s (30)
where s is the Laplace transform variable, and .omega..sub.c is a constant.
There is strong evidence in the literature that 90% of the signal strength
of human-machine interaction is characterized in this manner. This is
termed the "crossover" model and to a first order approximation, this is
the most widely accepted model of human performance in the literature
today.
Although the present invention has been described with regard to one
embodiment, those skilled in the art will readily recognize that other
variations on the design of the present invention exist. Accordingly, the
inventors do not wish to be limited by the present specification, but only
by the appended claims.
Moreover, the present invention has been primarily described in terms as
having a primary application as device and method to detect tracking
errors, however, the present invention would be useful in a myriad of
other applications.
Top